I have an inexpensive motion sensing light on the outside of my house, which is on the same circuit as a 120V thermostatically controlled duct fan that pulls warm house air into the space (it's an arctic entryway / mudroom). Whenever the fan clicks off, the motion sensing light turns on as though it detected motion. I don't have any other circuits available in the space, so I'm wondering what my options are for cleaning up the power, or if a more expensive motion sensor is going to be more able to handle the electrical conditions.
Here is some guidance to help you isolate whether the problem is electrical in nature.
You could run an experiment by opening the electrical box for the motion sensor. Then temporarily disconnect the sensor from the supply wires in the box and cap off those wires. Then wire the sensor to a short pig tail piece of cord that is one to two feet in length (0.5 meter). This pig tail would be a part of cheap extension cord that had been cut in half and use the end that has the male plug remaining.
Use care to make sure that the pigtail cord and the sensor power are NOT connected to any part of the existing in wall wiring. Not replace the sensor back on its normal mounting but let the pigtail cord hang out of the electrical box and down the wall. (Note it may require some finesse to route the core correctly so the sensor can be re-mounted without pinching the cord. Possibly a slightly longer screw will be required).
The next step is to utilize a long extension cord. If you do not have a long one with a length of 50 to 100 feet (up to 30 meters) you may have to borrow one or purchase one.
Connect the extension cord to the pigtail and route the extension cord off into the house and plug into another power outlet that is known to be on a separate circuit. Proceed to test the fan and sensor for normal operation and see of the interfering symptom still exists. This should determine if the sensor is responding to noise generated by the fan assembly.
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The motion sensor's circuits are probably being confused by a voltage spike caused by an inductive kick from the fan. The voltage levels in the device are disturbed, reversing some voltage comparison so that the light is activated. The problem can be attacked at either end. Containing the surge at or near the fan, or preventing its entry into the motion detector.
Perhaps the fan has no snubber mechanism in place to mitigate inductive kicks when the motor is switched off. Without schematics for the fan and its control circuitry, it's impossible to give a specific recommendation such as "get such and such type of diode and solder it across such and such points".
A suitable film capacitor connected across the power terminals of the fan maybe able to contain the spike, and would make for a very cheap fix. The capacitance doesn't have to be very large (I'm guessing, on the order of .0nnn microfarads), but the capacitor should have a decent voltage rating, of at least a few hundred volts (i.e. beyond the line voltage) so it can take the spike.
The small capacitance of the surge cap appears to be nearly an open circuit to 60 Hz power line AC (a very high impedance). But a voltage spike looks like high frequency content which passes through the cap. The cap will "take the edge off" the spike, so to speak. It just has to do that well enough so that the motion sensor isn't falsely triggered.